How to texture a racing helmet (with all its logos)
We don't know how this specific artist created the unwrapped/distorted image texture.


  Did the artist use a different UV (say project from the left view) and
  then baked those lines onto a new UV?


This is a common technique called Projection Painting which is widely used during texturing. Since I found no clear overviews in any answer, I will demonstrate the basic steps.


Create a UV map, I named mine uvmapUnwrapped and unwrap it, maximizing used space and minizing distorsion. As you noticed, one cannot add any images onto the current 2d uv layout with them being distorted.





Create a second UV map (the plus-icon) which places a logo (or other desired image) neatly onto the object. I loaded the Blender logo in the UV editor and found that unwrapping the subdivded cube from orthographic front view with Cylinder Projection worked best for this szenario. But there are plenty of other unwrapping methods. U




At this point, both images should be showing correctly on the object when their respective uv maps are active.


Select the object and enter Texture Paint Mode. Go to the Slots tab, choose Image as mode, select the uv layout image as canvas layout, which we're going to paint on an choose its matching UV map layout.
We could now paint on the object by drawing strokes on it in the 3D view.





Go to the Tools tab, select the clone brush. Check the box at clone from image/uv map. Select the logo image and its matching uvmap. You can now "draw" the logo onto the texture.